theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, a roton is an elementary excitation, or

quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...

, seen in

superfluid helium-4 Superfluid helium-4 is the superfluid form of helium-4, an isotope of the element helium. A superfluid is a state of matter in which matter behaves like a fluid with zero viscosity. The substance, which looks like a normal liquid, flows without ...

and

Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67&n ...

s with long-range dipolar interactions or spin-orbit coupling. The

dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...

of elementary excitations in this

superfluid Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...

shows a

linear Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...

increase from the origin, but exhibits first a maximum and then a minimum in

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

as the

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...

increases. Excitations with momenta in the linear region are called

phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...

s; those with momenta close to the minimum are called rotons. Excitations with momenta near the maximum are called maxons. The term "roton-like" is also used for the predicted

eigenmodes A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies ...

in 3D

metamaterials A metamaterial (from the Ancient Greek, Greek word Meta, μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally ...

using beyond-nearest-neighbor coupling. The observation of such a "roton-like" dispersion relation was demonstrated under ambient conditions for both acoustic pressure waves in a channel-based metamaterial at audible frequencies and transverse elastic waves in a microscale metamaterial at ultrasound frequencies.

Models

Originally, the roton spectrum was phenomenologically introduced by

Lev Landau Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His a ...

in 1947. Currently there exist

models A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

which try to explain the roton spectrum with varying degrees of success and fundamentality. The requirement for any model of this kind is that it must explain not only the shape of the spectrum itself but also other related observables, such as the

speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...

and

structure factor In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation ...

. Microwave and Bragg spectroscopy has been conducted on helium to study the roton spectrum.

Bose–Einstein condensation

Bose–Einstein condensation Bose–Einstein may refer to: * Bose–Einstein condensate ** Bose–Einstein condensation (network theory) * Bose–Einstein correlations * Bose–Einstein statistics In quantum statistics, Bose–Einstein statistics (B–E statistics) describe ...

of rotons has been also proposed and studied. Its first detection has been reported in 2018. Under specific conditions the roton minimum gives rise to a crystal solid-like structure called the

supersolid In condensed matter physics, a supersolid is a spatially ordered material with superfluid properties. In the case of helium-4, it has been conjectured since the 1960s that it might be possible to create a supersolid. Starting from 2017, a defin ...

, as shown in experiments from 2019.

References

Bibliography

* {{Authority control Quasiparticles Bose–Einstein condensates Superfluidity Lev Landau

Models

Bose–Einstein condensation

See also

References

Bibliography